IIRC, both in the book and the EE of the movie, the Witch King says "This is my hour!" and I take him at his word, the point being that I think the Nazgul become more powerful as Sauron rises and as they get closer to Mordor and the Shadow.

I still don't like the movie scene and agree that the book encounter is much better, but I don't think the Witch King on Weathertop (or in Crickhollow, for that matter) is in the same league as Witch King at the siege of Minas Tirith.